Abstract

In this note we study a certain formal group law over a complete discrete valuation ring F[[un-1]] of characteristic p > 0 which is of height n over the closed point and of height n-1 over the generic point. By adjoining all coefficients of an isomorphism between the formal group law on the generic point and the Honda group law Hn-1 of height n- 1, we get a Galois extension of the quotient field of the discrete valuation ring with Galois group isomorphic to the automorphism group Sn-1 of Hn-1. We show that the automorphism group Sn of the formal group over the closed point acts on the quotient field, lifting to an action on the Galois extension which commutes with the action of Galois group. We use this to construct a ring homomorphism from the cohomology of Sn-1 to the cohomology of Sn with coefficients in the quotient field. Applications of these results in stable homotopy theory and relation to the chromatic splitting conjecture are discussed.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1037-1077
Launched on MUSE
2003-09-30
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.